Number Series - Quantitative Aptitude - Aptitude question and answers

Explanation / Important formulas:

  • In a simple series, the difference between two consecutive numbers is constant
    • Example: 27, 24, 21, 18, __
    • [Rule: There is a difference of (-3) between each item. The missing number in this case is 15]
    • Example: 3, 4, 6, 9, 13, 18, __
    • [Rule: Add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2…etc In this case the missing number is 24]
  • Check whether adjacent numbers in the series change based on a logical pattern
    • Example: 2, 4, 12, 48, __
    • [Rule : Multiply the first number by 2, the second number by 3 and so on The missing number is 240]
  • See if you can find a rule that involves using two or more basic arithmetic functions (+, -, ÷, x). In the below series, the functions alternate in an orderly fashion
    • Example: 5, 7, 14, 16, 32, 34, __
    • [Rule: Add 2, multiply by 2 , add 2, multiply by 2 etc. the missing item is 68]
  • There can also be series, they difference themselves create a series:
    • Example : +2, /3, x4, -5
    • [Rule: The number advance by intervals of 1 and the arithmetic function change in an ordinary sequence here the next Arithmetic function will be 9(3+6=9)]

In a more complex series the differences between numbers may be dynamic rather than fixed, but there still is a clear logical rule. 

More Information: https://en.wikipedia.org/wiki/Series_(mathematics)

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Number Series - Question And Answers

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Question 1
Find the next number 2, 7, 28, 63,126, ____
A
196
B
215
C
217
D
225
Question 1 Explanation: 
1 cube+1 = 2
2 cube-1 = 7
3 cube+1 = 28
4 cube-1 = 63
5 cube+1 = 126
6 cube-1 = 215
Question 2
Find the odd man out 165,275,341,583,493
A
275
B
341
C
583
D
493
Question 2 Explanation: 
In the other numbers, second digit = First digit + third digit
Question 3
Which number comes next?

402, 388, 410, 396, 418, 404, ____

A
412
B
416
C
422
D
426
Question 3 Explanation: 
388+8 = 396 396+8 = 404
410+8 = 418 418+8 = 426
The two series are combined together
Question 4
Cara, a blue whale participated in a weight loss program at the biggest office. At the end of every month, the decrease in weight from original weight was measured and noted as 1, 2,6,21,86,445,2676. While Cara made a steadfast effort, the weight machine showed an erroneous weight once. What was that?
A
2676
B
2
C
445
D
86
Question 4 Explanation: 
This is a number series problem
1, 2,6,21,86,445,2676
The wrong term has to be found out
1 *1+1 = 2
2*2 + 2 = 6
6*3+3 = 21
21*4+4 =88
88*5+5 =445
Hence, 86 is wrong. It should be 88
Question 5
3, 22, 7, 45, 15, ? , 31
A
45
B
90
C
91
D
35
Question 5 Explanation: 
Combination of two series
3, 7, 15, 31
22, 45, ?
The number is doubled and 1 is added to it.
(45*2)+1 = 91
Question 6
19, 24, 20, 25, 21, 26, ?
A
22
B
27
C
23
D
28
Question 6 Explanation: 
This is a combination of two series
19,20,21,22, and
24, 25, 26...
Question 7
What is the missing number in this series?

8  2  14  6  11 __  14  6  18  12

A
7
B
8
C
9
D
10
Question 7 Explanation: 
The sum of the first and last number is 20
The sum of the second and second from last number is 20
In this way, 11+9 = 20
Question 8
Which number comes before 30 in the below series?

1, 2, 3, 6, 7, 14, __,30,.....

A
15
B
16
C
17
D
18
Question 8 Explanation: 
Combination of two series
1, 3, 7, ?
2, 6, 14, 30
1+2 = 3
3+4=7
7+8 = 15
Question 9
1 4 9?

1 2 3 4

2 4 6 ?

A
16 and 8
B
36 and 4
C
25 and 5
D
49 and 7
Question 9 Explanation: 
The number in the first row is square number
The numbers in the third row are multiples of 2
So, 16 and 8
Question 10
2,5,9,19,37,
A
76
B
75
C
74
D
72
Question 10 Explanation: 
The pattern is *2+1,*2-1,*2+1,*2-1...
Missing number = 37*2+1 = 75
Question 11
(1/9), (1/3), 1, __ , 9
A
2/3
B
3
C
6
D
27
Question 11 Explanation: 
Each number is multiplied by3
1*3 = 3
Question 12
3, 8, 6, 14, ?, 20
A
11
B
10
C
8
D
9
Question 12 Explanation: 
3, 6,
8, 14, 20...
3+3 = 6
6+3 = 9
Question 13
1, 3, 3, 6, 7, 9,  ?, 12,21
A
10
B
11
C
13
D
21
Question 13 Explanation: 
1, 3, 7, ? , 21
3, 6,9,12
1+2 = 3
3+4 =7
7+6 = 13
13+8 = 21
Question 14
0, 6, 24, 60, 120, ?
A
210
B
240
C
250
D
180
Question 14 Explanation: 
0*1*2 = 0
1*2*3 = 6
2*3*4 = 24
3*4*5 =60
4*5*6 = 120
5*6*7 = 210
Question 15
134, 245,356,467
A
579
B
578
C
568
D
478
Question 15 Explanation: 
Each term is obtained by adding 111 to the preceding term
Missing number = 467+111 = 578
Question 16
3, 12, 27, 48, 75, 108, (........)
A
147
B
162
C
183
D
192
Question 16 Explanation: 
The number is 3*12, 3*22, 3*32, 3*42, 3*52, 3*62...
Missing number = 3*72 = 3*49 = 147
Question 17
5, 6, 9, 15,_ ,40
A
21
B
25
C
27
D
33
Question 17 Explanation: 
The pattern is +1, +3, +6...
i.e +1, +(1+2), +(1+2+3),....
Missing number = 15 + (1+2+3+4) = 25
Question 18
97, 86, 73, 58, 45
A
34
B
54
C
55
D
56
Question 18 Explanation: 
The pattern is -11, -13, -15, - 13.
Missing number = 45 – 11 = 34
Question 19
0.5, 0.55, 0.65, 0.8,
A
0.9
B
0.82
C
1
D
0.95
Question 19 Explanation: 
The pattern is +0.05, 0.10,+0.15,....
Missing number = 0.8+0.20 = 1
Question 20
1, 2, 5,12,27,58,121
A
246
B
247
C
248
D
249
Question 20 Explanation: 
The pattern is *2+0, *2+1,*2+2, *2+3, *2+4, *2+5,.....
Missing number = 121*2+6 = 248
Question 21
462, 420, 380, 306
A
322
B
332
C
342
D
352
Question 21 Explanation: 
The pattern is -42, -40...
Missing number = 380 – 38 = 342
Question 22
34, 18, 10, 6, 4
A
0
B
1
C
2
D
3
Question 22 Explanation: 
Each term is divided by 2 and then increased by 1 to obtain the next term
Missing term = (4/2) + 1 = 3
Question 23
5, 16, 49, 104
A
115
B
148
C
170
D
181
Question 23 Explanation: 
The pattern is +11, +33, +55...
i.e..., +(11*1), +(11*3), +(11*5),....
Missing number = 104 + (11*7) = 181
Question 24
95,115.5, 138, 189
A
154.5
B
162.5
C
164.5
D
166.5
Question 24 Explanation: 
The pattern is +20.5, +22.5...
Missing term = 138+24.5 = 162.5
Question 25
2, 3, 8, 63,(......)
A
1038
B
1998
C
3008
D
3968
Question 25 Explanation: 
Each term in the series is one less than the square of the preceding term
Thus, 22 -1 = 3,
32 -1 = 8,
82 – 1 = 63
Missing number = (63)2 -1 = 3969 – 1 = 3968
Question 26
8, 10, 14, 18,34,50,66
A
24
B
25
C
26
D
27
Question 26 Explanation: 
The pattern is +2, +4, +4 ...+16, +16
Missing number = 18 + 8 = 26
Question 27
2, 15 41, 80
A
111
B
120
C
121
D
132
Question 27 Explanation: 
The pattern is +13, +26, +39...
Missing number = 80+52 = 132
Question 28
1, 3,4,8,15,27
A
37
B
44
C
50
D
55
Question 28 Explanation: 
The sum of any three consecutive terms of the series gives the next term
Thus, 1+3+4 = 8;
3+4+8 = 15;
4+8+15 = 27 and so on.
Missing number = 8+15+27 = 50
Question 29
3, 6, 5,20,7,42,9,
A
54
B
60
C
66
D
72
Question 29 Explanation: 
The sequence is a combination of two series:
I. 3,5,7,9 and
II. 6, 20, 42, (....)
The pattern is followed in II is +14, +22...
Missing number = 42 + 30 = 72
Question 30
21, 25,33,49,81
A
145
B
129
C
113
D
97
Question 30 Explanation: 
The pattern is +4, +8, +16, +32...
i.e. +22, +23, +24, +25...
Missing number =81+26 = 81+64 = 145
Question 31
66, 36, 18
A
3
B
6
C
8
D
9
Question 31 Explanation: 
Each number is the series is the product of the digit of the preceding number
Thus, 6*6 = 36,
3*6 = 18 and so on.
Question 32
3, 6, 18, 72
A
144
B
216
C
288
D
360
Question 32 Explanation: 
The pattern is *2, *3, *4...
Missing number = 75 * 5 = 360
Question 33
4, 5, 9, 18, 34, (......)
A
43
B
49
C
50
D
59
Question 33 Explanation: 
The pattern is +1, +4, +9, +16...
i.e.., +12, +22, +32, +42....
Missing number = 34+52 = 34+25 = 59
Question 34
1, 2, 3,6,9,18,54
A
18
B
27
C
36
D
81
Question 34 Explanation: 
The number are alternately multiplied by 2 and 3/2
Thus, 1*2 = 2,
2*3/2 = 3,
3*2 = 6,
6 * 3/2 = 9 and so on
Missing number = 18 * 3/2 = 27
Question 35
19, 2, 38, 3, 114, 4
A
228
B
228
C
352
D
456
Question 35 Explanation: 
The sequence is a combination of two series:
I. 19, 38, 114, (.....) and
II. 2, 3, 4
The pattern followed in I is *2, *3...
Missing number = 114*4 = 456
Question 36
0,2,8,14,34
A
24
B
22
C
20
D
18
Question 36 Explanation: 
The number is 12-1, 22-2, 32 -1, 42-2...
Missing number = 52 -1 = 24
Question 37
121,225,361,
A
441
B
484
C
529
D
729
Question 37 Explanation: 
The number is 112, 152,192...
i.e. 112, (11+4*1)2, (11+4*2)2...
Missing number = (11+4*3)2= (23)2 = 529
Question 38
0.5, 1.5, 4.5, 13.5
A
45.5
B
39.5
C
30.5
D
40.5
Question 38 Explanation: 
Each term of the series is obtained by multiplying the preceding term by 3
Missing number = 13.5*3 = 40.5
Question 39
Each term of the series is obtained by multiplying the preceding term by 3

Missing number = 13.5*3 = 40.5

A
9
B
11
C
13
D
15
Question 39 Explanation: 
Each term of the series is obtained by multiplying the preceding term by 3
Missing number = 13.5*3 = 40.5
Question 40
1,6,15,45,66,91
A
25
B
26
C
27
D
28
Question 40 Explanation: 
The pattern is +5, +9...+ 21, +25
Missing number = 15+13 = 28
Question 41
3, 7,15,31,63
A
92
B
115
C
127
D
131
Question 41 Explanation: 
Each number in the series is the preceding number multiplied by 2 and then increased y 1
Thus, (3*2) + 1 = 7
(7*2)+1 = 15
(15*2) +1 = 31 and so on
Missing number = (63*2) + 1 = 127
Question 42
5, 9,17,29,45
A
60
B
65
C
68
D
70
Question 42 Explanation: 
The pattern +4, +8, +12, + 16...
Missing number = 45+20 =65
Question 43
2,5,9,20,27
A
14
B
16
C
18
D
24
Question 43 Explanation: 
The pattern is +3, +4...
Missing number = 9+5 = 14
Question 44
1,9,17,33,49,73
A
97
B
98
C
99
D
100
Question 44 Explanation: 
The pattern +8, +8, +16, +24...
Missing number = 73+24 = 97
Question 45
3, 9, 27, 81,
A
324
B
243
C
210
D
162
Question 45 Explanation: 
Each term of the given series is obtained by multiplying its preceding term by 3
Missing number = 81*3 = 243
Question 46
1, 6,13,22,33
A
44
B
45
C
46
D
47
Question 46 Explanation: 
The pattern is +5, +7, +9, +11....
Missing number = 33+13 = 46
Question 47
22, 21, 23,22,24,23,
A
22
B
24
C
25
D
26
Question 47 Explanation: 
This is a combination of two series
22,23,24,25, and
21,22,23,24...
Hence, 25 comes next
Question 48
1000, 200, 40, ____
A
8
B
10
C
15
D
20
Question 48 Explanation: 
Each number is divided by 5
40/5 = 8
Question 49
5.2, 4.8, 4.4, 4  , ____
A
3
B
3.3
C
3.5
D
3.6
Question 49 Explanation: 
0.4 is subtracted from every number
3.6 comes next
Question 50
80, 10, 70, 15, 60, ___
A
20
B
25
C
30
D
50
Question 50 Explanation: 
This is a combination of two series
80,70,60,50.... and
10, 15, 20 ,....
Hence, 20 comes next
Question 51
8, 12, 9, 13, 10, 14, 11, __  , __
A
14, 11
B
15, 12
C
8, 15
D
15, 19
Question 51 Explanation: 
It is a combination of two series
8, 9,10,11,12, and
12,13,14,15...
Hence, the answer is 15, 12
Question 52
1 4 9 ?

1 2 3 4

2 4 6 ?

A
16 and 8
B
16 and 8
C
16 and 8
D
49 and 7
Question 52 Explanation: 
The numbers in the first row are square number
The numbers in the third row are multiples of 2
So, 16 and 8
Question 53
Which number comes before 30 in the below series?

1, 2, 3, 6, 7, 14 ,__,30,....

A
15
B
16
C
17
D
18
Question 53 Explanation: 
1, 2, 7, ?
2, 6, 14, 30
1+2 = 3
3+4 =7
7+8 =15
Question 54
What is the missing number in this series?

8  2  14  6  11  _  14  6  18  12

A
7
B
8
C
9
D
10
Question 54 Explanation: 
The sum of the first and last number is 20
The sum of the second and second from last number is 20
In this way, 11+9 = 20
Question 55
11, 14, 12, 15, 13, 16,  ? ,
A
13
B
14
C
15
D
17
Question 55 Explanation: 
This is a combination of two series
11,12,13,14... and
14, 15, 16...
Question 56
19, 24, 20, 25, 21, 26,  ?
A
22
B
27
C
23
D
28
Question 56 Explanation: 
This is a combination of two series
19,20,21,22,... and
24, 25, 26,...
Question 57
3, 22, 7, 45, 15  ,?, 31
A
45
B
90
C
91
D
35
Question 57 Explanation: 
Combination of two series
3, 7, 15, 31
22, 45,?
The number is doubled and 1 is added to it.
(45*2)+1 = 91
Question 58
70, 54, 45, 41, ____
A
42
B
40
C
38
D
39
Question 58 Explanation: 
70 -16 = 54
54-9 = 45
45-4 = 41
41-1 = 40
Question 59
5,  ?,  15, 75, 525,4725
A
5
B
8
C
10
D
1
Question 59 Explanation: 
5 x 1= 5
5 x3 =15
15 x 5 = 75
75 x 7 = 525
525 x 9 = 4725
Hence, the answer is 5
Question 60
1, 7, 8, 49, 50, 56, 57, 343, ___
A
344
B
2401
C
347
D
1221
Question 60 Explanation: 
1*7 = 7
7+1 = 8
7*7= 49
49+1= 50
8*7= 56
56+1= 57
49*7 = 343
343+1 = 344
Question 61
1, 4, 2,8,6,24,22, 88, ___
A
90
B
86
C
84
D
176
Question 61 Explanation: 
The first number is multiplied by 4 and the next number is subtracted by 2. This is repeated.
88-2 = 86
Question 62
1.3, 2.2, 3.1, 4.0, 4.9, __
A
6
B
5.8
C
5.5
D
5.2
Question 62 Explanation: 
Addition series
0.9 is added to each number
4.9+0.9 = 5.8
Question 63
48, 44, 46, 42, 44, 40, ?
A
46
B
38
C
44
D
42
Question 63 Explanation: 
4 is subtracted from the first number

2 is added to the next number

This is repeated

40+2 = 42
Question 64
17, 19, 17, 17, 17, 15, 17, 13, __
A
17
B
15
C
13
D
11
Question 64 Explanation: 
In the series
19, 17,15,13,11...
17 is present between all numbers
So the next number in the series is 17
Question 65
4, 3, 5, 4, 6, 5, 7, 6, ?
A
4
B
8
C
6
D
5
Question 65 Explanation: 
The first number is subtracted by 1
The next number is added by 2
6+2 = 8
Question 66
8, 15, 24, 35, 48, 63, ?
A
70
B
80
C
75
D
88
Question 66 Explanation: 
The difference between consecutive numbers increased by 2
8+7
15+9
21+11
............
63+17 = 80
Question 67
5, 4, 6, 3, 7, 2, 8, 1,?
A
-5
B
6
C
10
D
9
Question 67 Explanation: 
5-1, 4+2, 6-3, 3+4, 7-5, 2+6, 8-7, 1+8 = 9
It can also be taken as the combination of the two series
5, 6,7,8,9, and
4, 3,2,1,0...
Question 68
240,240, 120, 40,10,___
A
5
B
4
C
2
D
1
Question 68 Explanation: 
240 / 1, 240/2, 120/3, 40/4, 10/5 = 2
Question 69
1, 4, 27, 4, 25, 216, 7, ___
A
8
B
64
C
49
D
81
Question 69 Explanation: 
1, 2 square, 3 cube, 4, 5 square, 6 cube, 71, 8 square....

Question 70
2, 4, 7,12,19,30,
A
43
B
42
C
45
D
44
Question 70 Explanation: 
The difference between consecutive numbers is prime
2, 3, 5,7,11
The next prime number is 13
30+13 = 43
Question 71
Look at this series: 2,1,(1/2),(1/4),.....

What number should come next?

A
(1/3)
B
(1/8)
C
(2/8)
D
(1/16)
Question 71 Explanation: 
This is a simple division series; each number is one-half of the previous number
In other term to say, the number is divided by 2 successively to get next result
4/2 = 2
2/2 = 1
½ = ½
(1/2)/2 = ¼
(1/4)/2 = 1/8 and so on
Question 72
The series below:

7, 10,8,11,9,12.... What number should come next?

A
7
B
10
C
12
D
13
Question 72 Explanation: 
This is a simple alternating addition and subtraction series. In the first pattern, 3 is added: in the second, 2 is subtracted.
Question 73
Series: 36, 34,30,28,24, what number should come next?
A
20
B
22
C
23
D
26
Question 73 Explanation: 
This is an alternating number subtraction series.
First, 2 is subtracted then 4, then 2 and so on
Question 74
The series 53, 53, 40,40,27,27... What number should come next?
A
12
B
14
C
27
D
53
Question 74 Explanation: 
In this series, each number is repeated, then 13 is subtracted to arrive at the next number
Question 75
Find next number of the following sequence 124, 62, 60, 30, 28, 14   ?
A
7
B
8
C
12
D
13
Question 75 Explanation: 
124/2=62 & 62-2=60
60/2=30 & 30-2=28
28/2=14 & 14- 2=12
Question 76
Find the sum of all the terms in the series 1, ½, ¼ ……….
A
2
B
3
C
4
D
cannot be determined
Question 76 Explanation: 
Sum of the infinite G.P = a/1-r (here a=1st term, r= ratio)
=1/ (1-1/2) =2
Question 77
The series 80, 10,70,15,60, what number should come next?
A
20
B
25
C
30
D
50
Question 77 Explanation: 
This is an alternating addition and subtraction series. In the pattern, 10 is subtracted from each number to arrive at the next. In the second, 5 is added to each number to arrive at the next.
Question 78
The series: 2, 6, 18, 54... What number should come next?
A
108
B
148
C
162
D
216
Question 78 Explanation: 
This is a simple multiplication series. Each number is twice times more than the previous number.
Question 79
The series: 1.5, 2.3, 3.1, 3.9, what number should come next?
A
4.2
B
4.4
C
4.7
D
5.1
Question 79 Explanation: 
In this simple addition series, each number increases by 0.8
Question 80
The series: 14, 28, 20,40,32,64, what number should come next?
A
52
B
56
C
96
D
128
Question 80 Explanation: 
This is an alternating multiplication and subtraction series:
First, multiply by 2 and then subtract 8
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